If the White House thought the image of Obama allegedly skeet shooting would quiet critics they were sorely mistaken.

He’s full of skeet!

Gun owners lampooned President Obama as Elmer Fudd yesterday after the White House released a photo — in the middle of a fierce national firearms debate — of the commander-in-chief shooting clay targets at Camp David over the summer.

While the president’s shooting skills were being mocked, his own gun-control allies privately fretted that Obama risked being ridiculed as a phony for suddenly trying to portray himself as a friend of sportsmen and hunters. Or, conversely, that he was glorifying the use of guns.

The photo was taken last Aug. 4, on Obama’s 51st birthday.

The left-handed president, wearing goggles and ear protection, peers down the barrel of a shotgun while his left index finger pulls the trigger.

Bam! A spray of smoke shoots out of the rifle.

The White House released the photo to back up Obama’s recent statements that he shot skeet at Camp David, a claim that gun-rights advocates said they doubted.

Obama aides even coined a term for the skeptics — calling them “skeeters.”

“For all the skeeters, POTUS [president of the United States] shoots clay targets on the range at Camp David on Aug. 4, 2012,” White House Communications Director Dan Pfeiffer said in releasing the photo.